Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ The answer usually given is To gain full voting privileges, I have known the data of $\\pi_m(so(n))$ from this table The generators of so(n) s o (n) are pure imaginary antisymmetric n×n n × n matrices
How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof I'm not aware of another natural geometric object. You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do i get it
I have a potentially simple question here, about the tangent space of the lie group so (n), the group of orthogonal $n\times n$ real matrices (i'm sure this can be. Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter Assuming that they look for the treasure in pairs that are randomly chosen from the 80 Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$
OPEN
